Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations

Abstract

Our goal is to remedy the failure of symmetry-adapted coupled-cluster theory in the presence of strong correlation. Previous work along these lines has taken us from a diagram-level analysis of the coupled-cluster equations to an understanding of the collective modes which can occur in various channels of the coupled-cluster equations to the exploration of non-exponential wavefunctions in efforts to combine coupled-cluster theory with symmetry projection. In this manuscript, we extend these efforts by introducing a new, polynomial product wavefunction ansatz that incorporates information from symmetry projection into standard coupled-cluster theory in a way that attempts to mitigate the effects of the lack of size extensivity and size consistency characteristic of symmetry-projected methods. We describe the new approach in detail within the context of our previous efforts, explore some illustrative calculations, and consider one route for reducing the computational cost of the new method.

Geminal replacement models based on AGP

“…Some words about the correlated AGP models from a symmetry-projection point of view. When compared to other ideas developed in our group in the general area of combining symmetry breaking and restoration tools with correlation methods like coupled cluster theory 57 , the methods presented in this article fall under the general category of project-then-correlate, as opposed to correlate-then-project, an alternative that has also been pursued both for number 58 and spin 59 . AGP is not size consistent and the extensive component of the AGP energy is the same as that of its underlying BCS wave function.…”

Energy of fermionic ground states with low-entanglement single-reference expansions, and tensor-based strong-coupling extensions of the coupled-cluster method

“…Another possible tensor-based extension of the CC method uses the definition (9) for T and equations (12). This produces equations similar to the CC ones, though involving the CI coefficients instead of cluster operator amplitudes, which are closed by parametrizing the coefficients with LRTD.…”

“…The explicit form of equations (12) in terms of CI coefficients and Hamiltonian parameters, obtained using the definition (9) for T , are provided for the l ≤ 4 excitation coefficients in section VI. To derive those equations, instead of the standard approach of CC that use a special notation to express particle-hole normal-ordered operators, we have used a representation of H in terms of excited particles and holes operators which is described in section V. To parametrize the CI coefficients, the same type of LRTD-based representation as proposed for the cluster amplitudes, and described in section VII, could be used.…”

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

“…Moreover, according to Lestrange et al [7], these inconveniences originating from the use of the grid points can be mitigated by using an efficient algorithm and Lebedev integration grids. On the other hand, unfortunately, the PHF method is not size consistent [1], but Scuseria and co-workers has attempted to reduce the size consistency errors while exploring the origin of the errors [8,9].…”

“…On the other hand, unfortunately, the PHF method is not size consistent, [1] but Scuseria and co-workers have attempted to reduce the size consistency errors while exploring the origin of the errors. [8,9] On the other hand, to obtain a wave function of the desired spin multiplicity from an unrestricted Hartree-Fock (UHF) wave function, Mayer et al [10][11][12] already derived the (spin projected) extended Hartree-Fock (EHF) equations by using both Löwdin's spin projection operator and generalized Brillouin theorem [13][14][15] in the 1970s. It has been known that for small molecules, the EHF method yields good results, [12] but its computational cost is high due to its quite complicated equations.…”